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Journal of Business & Economics
Vol.6 No.1 (Jan-June 2014) pp. 1-22
1
Inflation Dynamics with Bounded Rationality
Zhao Tong
*
Sano Kazuo∗∗
Abstract
There is an unbalanced specification in the standard new Keynesian model.
In the model, stickiness is assumed in the price setting, and then an
individual firm has a fixed probability to change its price in any given
period, which means that the market is imperfect. On the other hand, an
individual firm is assumed to be one that can conduct profit maximization
and calculate the degree of nominal rigidity in the future completely. In
order to avoid this unbalanced specification, we suppose that firms choose
the price with bounded rationality. Concretely, we assume that firms refer to
lagged inflation in the price setting, which is one of the simplest forms to
express bounded rationality. We then obtain the hybrid new Keynesian
Phillips curve to express inflation dynamics, named the sticky price with
bounded rationality Phillips curve (SPBR).
1. Introduction & Empirical Literature
During the past two decades, significant improvements have been made
in theoretical and empirical analysis, relating to both price setting and
persistent inflation mechanisms. Although many studies have been developed
in terms of inflation models which are even used to formulate and evaluate
actual monetary policies, a number of questions have yet to be answered on
this topic. As Woodford (2007) stated, "Some argue that these two desiderate
*Zhao Tong, Associate Professor, Faculty of Integrated Arts and Sciences, Tokushima
University, Japan. Email: [email protected]. ∗∗Sano Kazuo, Professor, Department of Economics, Fukui Prefectural University, Japan.
Email: [email protected]
Acknowledgement: We would like to thank seminar participants at the Spring Meeting of the
Japanese Economic Association held at Doshisha University on 14 June 2014. In particular,
we would like to thank Ryo Kato for his helpful comments and suggestions.
Tong & Kazuo
2
remain in considerable tension with one another――that one cannot insist
upon optimizing foundations, at least under the current state of knowledge,
without substantial sacrifice of quantitative realism."
One critical topic regarding the gap between theoretical deduction and
empirical practice is how to treat lags and leads of inflation and output on the
actual one. There are no lagged terms in the standard new Keynesian model
or new Keynesian Phillips Curve (NKPC). However, a model with lagged
terms, called the hybrid new Keynesian model which is short for
microeconomic foundation, is being utilized, as well as by economists,
businessmen and econometric researchers, in macro econometric models of
central banks and international financial institutions because of its good
performance on real data.
The history of economics reveals that a sensible principle is practical
rather than theoretical. Fuhrer (1997) emphasizes the importance of
backward-looking behavior in price specifications in the Taylor’s contract
model, and concludes that a mixed backward-looking/forward-looking price
specification provides more reasonable behavior on empirical performance. It
is well known that there is a strong correlation between actual inflation and
lags (e.g., Mankiw, 2001; Gordon, 1997). Fuhrer and Moore (1995) coin a
new technical term, “inflation persistence”, to explain this phenomenon. To
resolve the puzzle of inflation persistence, several preceding theoretical
studies have been performed.
Christiano et al. (2005) present a hybrid new Keynesian Phillips curve to
analyze inflation and output persistence with a special assumption. The
assumption is that some firms that cannot change their prices do not maintain
it, but rather automatically discount prices according to the last period’s
inflation rate. However, as Angeloni et al. (2006) pointed out, such an ad hoc
assumption as an automatic backward-looking indexation cannot be
consistent with macroeconomic evidence. In support of this, Woodford
(2007) argues that "the model's (Christiano et al, 2005) implication that
individual prices should continuously adjust in response to changes in prices
Inflation Dynamics with Bounded Rationality
3
elsewhere in the economy flies in the face of the survey evidence."
Gali and Gertler (1999) allow for a subset of firms using a backward-
looking rule to set prices to obtain the hybrid new Keynesian Phillips curve.
They maintain that the hybrid new Keynesian Phillips curve is more
persuasive than the New Keynesian Phillips curve in terms of fitting actual
data. Their work, however, is exposed to incisive criticism of both their
theoretical approach and empirical method1. Although lags of inflation are
crucial to explain the current one, the simple rule-of-thumb behavior
assumption omits theoretical rationality. In fact, it is irrational to assert that
firms set their prices by the backward-looking rule. From the perspective of
firms profit maximization or cost minimization, menu cost will be at least
saved by maintaining prices, rather than changing them.
Mankiw and Reis (2002) propose another mechanism. They examine a
dynamic price model based on an assumption that information disseminates
slowly throughout the population, i.e., "sticky-information" compared to
"sticky-price". This assumption allows the model to obtain a lagged inflation
term in NKPC. They contend that the maximum effect of monetary policy
shocks will appear several periods later. However, as Dupor and Tsuruga
(2005) claimed, the result of this sticky-information model depends largely
on the diffusion structure of information. Thus, in the case in which the
diffusion structure of information is assumed in a fixed duration, such as
Taylor (1979), the persistent and hump-shaped inflation and output dynamics
will disappear.
This paper proposes a new model to explain inflation dynamics. The
essence of the model is that firms choose the price with bounded rationality.
In the standard NKPC model based on Calvo (1983), the aggregate price
index is a weighted average of the price charged and not-charged by firms,
which means that there is a nominal rigidity of price, which is one of the
most important features of the NKPC model. On the other hand, firms choose
1The detailed argument on the empirical method refers to Rudd and Whelan (2005), Linde
(2005) and Gali, Gertler and Lopez-Salido (2005).
Tong & Kazuo
4
an optimal price based on monopolistic competition, which implies that the
firms are implicitly assumed to be market-clearing ones. It is unbalanced for
an individual firm to be treated as one that can conduct profit maximization
and calculate the degree of nominal rigidity in the future completely, while
sticky-price is also assumed in the model simultaneously.
Blanchard and Gali (2007) introduce real wage rigidities -one of bounded
rationality of the market- in the model. They then derive a simple
representation of inflation as a function of lagged and expected inflation, the
unemployment rate, and the change in the price of non-produced inputs.
Although their model’s specification differs greatly from that of our model,
the concept of its hypothesis is similar to ours.
Mishkin (2007) argues that the recent changes in inflation dynamics are
less persistent and more likely to gravitate to a trend level, and expectations
have become better anchored. Bernanke (2010) and Donald Kohn (2010)
hold a similar view. Ball and Mazumdar (2011), adding the hypothesis of
anchored inflation expectations into the traditional Phillips curve, examine
inflation dynamics in the U.S. since 1960 and forecast the inflation rate
during the Great Recession2. Although they examine the traditional Phillips
curve, they provide us with a number of discerning ideas. For example, the
fact that the hypothesis of anchored expectations can refine the prediction of
inflation dynamics suggests that firms are not perfect market-clearing ones.
We add expectations with bounded rationality into the model to obtain the
hybrid new Keynesian Phillips curve.
In the next section, we present our model in detail. We call the model the
sticky-price with bounded rationality (SPBR), in contrast with the NKPC.
Section II shows the simulation and estimation of the model, and examines
inflation dynamic properties. Section III analyzes bounded rationality
2 For refining the prediction of inflation dynamics, Ball and Mazumdar (2011) also
modify two points of Phillips curve: 1) measuring core inflation with the weighted
median of consumer price inflation rate across industries; and 2) allowing the slope
of Phillips curve to change with the level of variance of inflation.
Inflation Dynamics with Bounded Rationality
5
compared to sticky price, and explains why bounded rationality needs to be
introduced in the model. We conclude our paper in section IV.
2. Sticky Price with Bounded Rationality Model
We will directly introduce the key aggregate relationships, rather than
working through the details of the derivation. Concerning the firm’s desired
price at period, the price would maximize profit. The desired price can be
presented as follows with all variables expressed in logs:
ttt ypp α+=∗ (1)
where ∗tp is the desired price level at time t ; tp
is the overall price
level; and ty interprets the output gap for potential output, which is
normalized to zero here. The parameter α is the degree of the output gap on
the desired price level, and 0>α . This equation shows that the firm’s
desired price depends on the overall price level and output gap positively,
and that the gap of price level tt pp −∗ rises in economic booms and falls in
recessions. Not deriving the equation from a firm’s profit maximization, we
follow our specification, which is consistent with that of Mankiw and Reis
(2002)3.
In this model, we assume the sticky-price mechanism as Calvo (1983),
i.e., each firm has a fixed probability ρ in any given period that the firm
may adjust its price during that period and, hence, the probability that the
firm must keep its price unchanged is ρ−1 , where 10 ≤≤ ρ . This
probability is independent of the time elapsed since the last price revision.
Firms are identical ex ante, except for the differentiated product that they
produce and for their pricing history. We assume that each firm faces a
3 The baseline specification of this model is in accordance with the standard new Keynesian
model, which assumes that each firm is identical and competes monopolistically following
Blanchard and Kiyotaki (1987).
Tong & Kazuo
6
conventional constant price elasticity of the demand curve for its product.
Then, the overall price level becomes as a weighted average of the lagged
price level 1−tp and the adjustment price level, tx as follows:
1)1( −−+= ttt pxp ρρ (2)
This sticky-price mechanism, one of the most important features of the
Calvo's model, implies that the market is imperfect. As the standard Calvo
model sets, firms do not set the adjustment price level tx to be equal to ∗tp ,
but side up the degree of stickiness of price and then set up a price as a
convex combination of the future adjustment price level, 1+tx , another of
crucial feature of Calvo's model. We can notice a contradiction between
these two specifications. The market is assumed to be imperfect, but each
firm is assumed to be a market-clearing one. In order to correct this
contradiction, we assume that firms are not market-clearing price-setters but
rather price-setters with bounded rationality. Considering the evidence of the
importance of the lagged inflation as mentioned above, firms set the
adjustment price level, tx as follows:
( ) [ ]∑∞
=+−
∗++−
∗ +−=−++=0
111 )1()1(j
jtjt
j
tttttt pExEpx βπρρρβπρ (3)
The adjusted price level of firms is affected by the desired price level,
∗tp and also influenced by the lagged inflation 1−tπ , which presents the
bounded rationality of firms. The parameter β represents the degree of
bounded rationality, which means the relative degree to the lagged inflation
relevant to the desirable price level, and satisfies 0>β ; then, the ratio
of 1−tπ to ∗tp is β
ββ ++ 11
1 : . The right side of the second equal sign is one that
is solved forward iteratively.
Inflation Dynamics with Bounded Rationality
7
This specification is the simplest one for bounded rationality. We can
also assume one that it includes the anchor effect, such as is assumed in Ball
and Mazumdar (2011), to express bounded rationality of firms:
( ) 11 )1( +−∗ −+++= tttttt xEApx ρϑβπρ
where tA explains the anchor effect. The ratios of
∗tp to 1−tπ to tA
then become ϑβϑ
ϑβ
β
ϑβ ++++++ 1111 :: , respectively. This specification, however,
does not affect any qualitative conclusions. For simplicity, we maintain the
simple specification as Equation (3).
With some tedious algebra, which can be found in detail in Appendix A,
we yield the following equation for inflation:
1
22
111
−+−
+−
+= ttttt yE πρ
βρ
ρ
αρππ (4)
We call this equation the sticky-price with bounded rationality Phillips
curve (SPBR). The actual inflation depends not only on the actual output and
inflation rate expectation, but also on the lagged inflation, a hybrid new
Keynesian Phillips curve. The coefficient of lagged inflation depends on the
frequency of price adjustment, ρ and the degree of bounded rationality β .
The coefficient of output gap depends on ρ and the degree of output gap on
desired price levelα . Repeatedly, we obtain the SPBR deriving from two
underlying assumptions, the sticky-price mechanism and the price-setting
with bounded rationality. These assumptions imply that both sides of the
market and firms are imperfect.
3. Simulation and Estimation
We have presented the SPBR, and will now examine its dynamic
Tong & Kazuo
8
properties. To achieve this and present a comparison with previous studies,
we first need to introduce a hybrid Phillips curve differing from Equation (4),
as follows4:
ttbttft yE λπφπφπ ++= −+ 11 (5)
where λ is a coefficient for output gap, and can be regarded as ραρ
−1
2
related to Equation (4); and parameter fφ and bφ represent the contributive
degree of expected and lagged inflation to the actual one, respectively.
Although Equation (4) and Equation (5) are not strictly the same, using the
parameters in Equation (4), we can regard the relative ratio of the two
parameters as: ωω
ω ++ 11
1 : , ρβρω −≡1
2
where ρβρω −≡1
2
To complete the model, we need to adopt an expectational IS curve of a
hybrid form, as follows:
( )111 +−+ −−+= ttttbttft EiyyEy πδϕϕ (6)
where ti is the nominal interest rate; δ is the inverse of the degree of
relative risk aversion; and fϕ and bϕ are the parameters, satisfying
10 << fϕ and 10 << bϕ . Equation (6) can be obtained from the Euler 's
equation using a habit formation utility function.
We select 5.1=δ and 1.0=α , as usual for simulation, to display the
impulse responses of inflation and output dynamics to a particular shock. We
select 5.0== bf φφ and 5.0== bf ϕϕ for two reasons. First, the sum of
parameters fφ and bφ are set equal to 1, as presented by previous studies.
4 Equation (3) is almost the same as Equation (4). Beginning with a slightly different setup, we
can get the equation easily (e. g., Walsh, 2005, Chapter 8).
Inflation Dynamics with Bounded Rationality
9
Second, following our GMM estimation as described next, the values of
fφ and bφ are about 0.5. Although many previous studies, such as Gali and
Gertler (1999), the pioneer study using GMM, estimate that the forward-
looking coefficient, fφ is larger than the backward-looking one, bφ and the
values of fφ and bφ are about 0.6 and 0.4, respectively, the selection of
instrument variables in their models is arbitrary. We will discuss this topic in
detail next and in Appendix B. Moreover, Kurmann (2007), using the
Maximum-Likelihood (ML) approach, obtains an estimation result that the
value of fφ is 0.542 using same data set as Gali and Gertler (1999). Jondeau
and Bihan (2005) report that the values of fφ of the U.S. are 0.480 with
output gap and 0.525 with real ULC; those of the Euro area are 0.496 and
0.540, respectively.
The model including Equation (5) and (6) implies that as long as the
central bank is able to affect the real interest rate through its control of the
nominal interest rate, monetary policy can affect real output. The changes in
real interest rate alter the optimal time path of consumption. Firstly, we
consider a sudden drop in the level of aggregate demand. Fig. 1 illustrates the
impact of a monetary policy shock, a decrease in the nominal interest rate ti
in the model; policy rule agrees with the Taylor rule as follows:
tttt yqqi υπ ++= 21
The parameter values are 5.01 =q and 5.12 =q , as usual. In addition,
the policy shock, tυ in the policy rule is assumed to follow an AR(1) process
given by ttt εξυυ += −1 , with 8.0=ξ . The impulse response that we select
is that the nominal interest rate; ti unexpectedly falls by 10 percent at time
zero.
Fig. 1 shows that the apparent fall in the nominal interest rate causes
Tong & Kazuo
10
Fig.1
inflation and the output gap to rise immediately, and then gradually dissipate
over time. The difference between our model and the new Keynesian model
is when we examine the response of inflation. It is well-known that the
maximum impact of a rise in inflation occurs immediately in the new
Keynesian model; whereas, the maximum impact occurs at five quarters in
our model. Thus, inflation persistence could be well described. The output
gap rises immediately and converges to zero over time, although it falls to a
slight minus.
We then consider a sudden shock in the money supply. Fig. 2 shows
inflation and the output gap dynamic with monetary rule as follows:
ttt myi µδ += 1 ;
ttt MM ωτ +∆=∆ +1 ;
111 +++ +∆−= tttt Mmm π
where ttt mpM =− . The policy shock is assumed to follow an AR(1)
Inflation Dynamics with Bounded Rationality
11
process. The parameter values are; 2=µ , 5.1=δ and 8.0=τ . The impulse
response that we select is that the nominal money supply; tM∆ unexpectedly
increases by 10 percent at time zero.
Fig.2
The quantitative easing policy in the money supply brings about the
output gap and growth of inflation, which gradually dissipates over time. As
same as the case of Taylor rule, the difference between our model and the
new Keynesian model is apparent when the response of the inflation rate is
examined. Contrary to the new Keynesian model that raises the maximum
impact immediately, the maximum impacts on inflation and output gap occur
at five quarters in our model.
Inflation persistence has been well described in our model. Although the
maximum impact on inflation occurs five quarters after shock, which is
slightly quicker than the actual data (Fuhrer and Moore, 1995), it is easy to
change the peak period at and after eight quarters by a simple adjustment
within the reasonable parameters range.
We now present and discuss the GMM estimate of the hybrid models
described above. Using the GMM technique, we report parameters in Table 1
Tong & Kazuo
12
Table 1
Estimation of the Hybrid Philips Curve by GMM
bφ fφ ULCλ GDPλ
Case I: U.S. (1960:Q1-1997:Q4)
ULC
0.355 0.627 0.014
(0.039) (0.023) (0.006)
GDP GAP
0.323 0.685 -0.006
(0.047) (0.051) (0.003)
Case II: US (1960:Q1-2013:Q2)
ULC
0.505 0.515 -0.007
(0.015) (0.018) (0.008)
GDP GAP
0.518 0.498 0.010
(0.018) (0.016) (0.010)
Case III: Euro area (1970:Q1-1999:Q4)
ULC
0.387 0.608 0.000
(0.059) (0.059) (0.005)
GDP GAP
0.367 0.628 0.121
(0.091) (0.091) (0.094)
Note: in all cases, the dependent variable is quarter inflation measured using the GDP
Deflator. Standard errors are shown in brackets. Case I is a result of the U.S. from 1960:Q1 to
1997:Q4, cited by Gali, Gertler and Lopez-Salido (2005)'s Table 1. Case III is a result of the
Euro area from 1970:Q1 to 1999:Q4, cited by Jondeau and Le Bihan (2005)'s Table 1. In Case
II, the instrument set includes a constant term, one lag and lead inflation rate, and current real
UCL or output gap.
which estimate the hybrid new Keynesian Phillips curve as follows:
tulctftbt ULC⋅+⋅+⋅= +− λπφπφπ 11
tGDPtftbt y⋅+⋅+⋅= +− λπφπφπ 11
where ulcλ is a parameter when the explanatory variable is a real Unit Labor
Cost (ULC); and GDPλ is another parameter when the explanatory variable is
the output gap. Standard errors are shown in brackets. Case I is a result of the
U.S. from 1960:Q1 to 1997:Q4, cited by Gali, Gertler and Lopez-Salido
Inflation Dynamics with Bounded Rationality
13
(2005) Table 1. Case III is a result of the Euro area from 1970:Q1 to
1999:Q4, cited by Jondeau and Le Bihan (2005)'s Table 1.
The data that we use (Case II) is quarterly for the U.S. over the period of
1960:Q1 to 2013:Q2, drawn from OECD Business Sector Data for the U.S.
The inflation rate is the percent change of inflation measured using the GDP
Deflator. The output gap is the percent deviation of real GDP from its trend,
computed using the Hodrick-Prescott filter. The instrument set that we select
includes a constant term, one lagged and lead inflation, and the actual UCL
or output gap; whereas, Gali, Gertler and Lopez-Salido (2005) select an
instrument set that includes two lags of detrended output, real marginal costs
and wage inflation and four lags of inflation. Jondeau and Le Bihan (2005)
instrument set is a similar one. As Muth (1961) emphasized, the variance of
predicting error needs to be minimal. Since increasing extra lagged or lead
variables in the instrument set causes the variance to be bigger, which
violates rational expectations, we select an instrument set which is the
simplest one as above to keep its variance to a minimum. Appendix B gives
the theoretical explanation in detail.
Firstly, as Table 1 shows, the parameters of bφ and fφ are all
statistically significant with both real ULC and output gap in three case. This
indicates that the backward-looking inflation is important to the actual one,
as well as to the forward-looking one. Secondly, in each case, the estimates
of bφ and fφ , obtained by real ULC or output gap, are very close. Thirdly,
except for Case I with real ULC, the parameters of real UCL and output gap,
ULCλ and GDPλ , are not statistically significant; moreover, the value of
these parameters, compared with bφ and fφ , are very small. This evidence
suggests that the choice of forcing variable hardly influences the actual
inflation, which contradicts the claim by Gali and Gertler (1999) (Jondeau
and Le Bihan, 2005).
In Case II, we estimate that the value of bφ and fφ are around 0.5.
Tong & Kazuo
14
Comparing these values with those of Case I and III, the expected estimated
length, the differences arise from the setup of the instrument set as mentioned
above. Interestingly, using the ML approach, Jondeau and Le Bihan (2005)
report that the estimates of bφ and fφ for both the U.S. and Euro area are
very close to 0.5. Kurmann (2007) reports parallel estimates. This evidence
implies that the importance of the lagged inflation to the current one is the
same as that of the expected one. This contradicts the claim by Gali and
Gertler (1999), who state that the role of forward-looking inflation is more
important than that of the backward-looking one in the formation of inflation
expectations. Considering all of the evidence above, we believe that the value
0.5 of bφ and fφ are feasible values.
The estimated result of Blanchard and Gali (2007) is worthy of being
mentioned. They estimate that the coefficients of backward-looking inflation,
forward-looking inflation and unemployment rate are 0.66, 0.42 and -0.20,
respectively, with statistical significance. Although it is very remarkable to
obtain a large enough unemployment rate coefficient with statistical
significance, they use annual U.S. data on inflation and a four lags instrument
set of variables. Having several estimations with quarterly data of inflation
and unemployment rate consistent with Blanchard and Gali (2007), we
unfortunately cannot obtain a meaningful coefficient of unemployment rate.
To sum up these estimation results, the data and instrument set used in
empirical analysis have to be selected with extreme caution. On the other
hand, the estimation results, including our model, are far from satisfactory,
which suggests that theoretical and empirical analysis in this field must be
drastically improved.
4. Discussion
4.1 Sticky Price versus Bounded Rationality
We have presented the SPBR model, and have simulated and estimated
its dynamic properties. Now we return to theoretical considerations, and
Inflation Dynamics with Bounded Rationality
15
again investigate how the lagged and expected inflation affect the actual one
in our model, or similarly, how sticky price and bounded rationality affect
inflation.
Recalling Equation (3), it is easy to verify that Equation (4) will become
an NKPC form when 0=β . Define that D≡− ρ
βρ
1
2
and 0>D , and then
we can obtain 0<∂
∂
ρ
β
5 in the case that D is constant. Since the
parameters ρ and β signify the degrees of sticky price and bounded
rationality, the evidence indicates that the more stickiness is in the price
change, the more is the degree of bounded rationality in the price setting, and
vice versa. It is easy to understand this relation intuitively. It is intelligible
when a simple numerical example is shown. In the special case of 1=D ,
which corresponds to the case of 5.0== fb φφ as above, when 25.0=ρ ,
then 12=β ; when 5.0=ρ , then 2=β ; and when 67.0=ρ , then
75.0=β . When ρ is small, i.e., the probability in any given period that
the firm can adjust its price during that period is small, the degree of bounded
rationality, β becomes big, the firm will put more weight on the ratio on the
lagged inflation rather than on the desirable price level in the price setting.
The share on the desirable price level is 7.7 percent, and the share on the
lagged inflation is 92.3 percent when 12=β ; when 2=β , the share on
lagged inflation becomes 66.7 percent. Considering that the coefficient of the
lagged inflation term is around 1, when estimating the NKPC, the value of β
is not too big to be permissible.
4.2 The Source of SPBR
It is well known that since the lagged term of inflation exists, the delay in
5 Since D≡
− ρ
βρ
1
2 and 0>D , we can get
2
)1(
ρ
ρβ
−=
D , and then
0)1(2
4
2
<−−−
=∂
∂
ρ
ρρρ
ρ
β DD
Tong & Kazuo
16
inflation adjustment arises, and the maximum impact on inflation will occur
several quarters later, which can avoid the criticism of Ball (1994).
Moreover, as many previous studies pointed out, such as Gali and Gertler
(1999), the hybrid new Keynesian Phillips curve, compared with the NKPC,
exhibits good performance in empirical analysis.
When setting the price level, a firm must be concerned with the desirable
price level and an expected inflation in the NKPC model. In the SPBR
model, the firm is also concerned about the lagged inflation and other factors,
such as the anchor effect, which are not set in the model. The difference
between the two models is whether or not the bounded rationality of the firm
is admitted. In the case without bounded rationality in the price setting, the
firm is assumed to be a market-clearing one, which performs profit
maximization and evaluates the degree of nominal rigidity in the future
completely6. In the case with bounded rationality, however, the firm is
assumed to be not a perfect market-clearing one, which also performs profit
maximization and evaluates the degree of nominal rigidity; at the same time,
the firm is also assumed to refer to lagged inflation, which is the easily
obtainable and inexpensive information that the firm can hold.
Taking lagged inflation in the model, we can obtain the SPBR, a form of
the hybrid new Keynesian Phillips curve. The essence of the SPBR that we
want to emphasize is, as well as the lagged inflation in expecting the actual
inflation, the importance of the bounded rationality of the firm on inflation
dynamics. The bounded rationality of the firm, accompanying sticky price,
will rebalance the model without one-sided imperfection.
5. Conclusion
A great deal of advancement in theoretical and empirical analysis in both
price setting and sticky inflation has been achieved in the past two decades.
However, a number of questions have remained unanswered. A model that
6 That the firm cannot alter the price by sticky price results from the assumption that the
market is assumed to be imperfect.
Inflation Dynamics with Bounded Rationality
17
include the lagged terms, which is called the hybrid new Keynesian model
and short for microeconomic foundation, is being used extensively due to its
good performance on actual data. However, we realized that there is an
unbalanced specification in the standard new Keynesian model. In the model,
stickiness is assumed in the price setting, and then an individual firm has a
fixed probability to be able to change its price in any given period, which
means that the market is imperfect. On the other hand, an individual firm is
assumed to be one, which can conduct profit maximization and calculate the
degree of nominal rigidity in the future completely.
In order to avoid this unbalanced specification and obtain a model which
is suitable to the actual data, we suppose that firms choose the price with
bounded rationality. Concretely, we assume that firms refer to lagged
inflation in the price setting, one of the simplest forms to express bounded
rationality; thus, we obtain the hybrid new Keynesian Phillips curve to
express inflation dynamics, which we call the sticky price with bounded
rationality Phillips curve.
As previous studies proved with the hybrid new Keynesian model, the
SPBR possesses a remarkable feature compared with the NKPC, i.e.,
inflation persistence exists well. There is an interesting relation between
sticky price and bounded rationality, in which the more stickiness that is in
the price changing, the more is the degree of bounded rationality in the price
setting, and vice versa. This is easy to understand intuitively. Furthermore,
firms will place most weight of the ratio on the lagged inflation rather than
on the desirable price level, in the price setting.
Taking in the bounded rationality or its concrete form, lagged inflation in
the model, we obtain the SPBR. The essence of the SPBR that we want to
emphasize is, as well as the lagged inflation in expecting the actual inflation,
the importance of the bounded rationality of the firm on inflation dynamics.
References
Angeloni, I., Aucremanne, L., Ehrmann, M., Galí, J., Levin, A., Smets, F.
Tong & Kazuo
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(2006). New Evidence on Inflation Persistence and Price Stickiness in
the Euro Area: Implications for Macro Modeling. Journal of the
European Economic Association, 4, 562-574.
Ball, L.M., 1994. Credible Disinflation with Staggered Price Setting.
American Economic Review, 84(1), 282-289.
Ball, L.M., Mazumdar, S. (2011). Inflation dynamics and the Great
Recession. Brookings Papers on Economic Activity, 42(1), 337-405.
Branchard, O, Gali, J. (2007). Real Wage Rigidities and the New Keynesian
Model. Journal of Money, Credit and Banking, 39(1), 36-65.
Blanchard, O.J., Kiyotaki, N. (1987). Monopolistic Competition and the
Effects of Aggregate Demand. American Economic Review, 77(4), 647–
666.
Calvo, G.A. (1983). Staggered Prices in A Utility-Maximizing Framework.
Journal of Monetary Economics, 12(3), 383-398.
Christiano, L.J., Eichenbaum, M., Evans, C.L. (2005). Nominal Rigidities
and the Dynamic Effects of a Shock to Monetary Policy. Journal of
Political Economy, 113(1), 1-45.
Dupor, B., Tsuruga, T. (2005). Sticky Information: The Impact of Different
Information Updating Assumptions. Journal of Money, Credit and
Banking, 37(6), 1143-1152.
Fuhrer, J.C. (1997). The (Un)Importance of Forward-Looking Behavior in
Price Setting. Journal of Money, Credit and Banking, 29(3), 338–350.
Fuhrer, J.C., Moore G.R.. (1995). Inflation Persistence. Quarterly Journal of
Economics, 110(1), 127-159.
Galí, J., Gertler, M. (1999). Inflation Dynamics: A Structural Econometric
Inflation Dynamics with Bounded Rationality
19
Analysis. Journal of Monetary Economics, 44(2), 195-222.
Galí, J., Gertler, M., Lopez-Salido, J. (2005). Robustness of the Estimates of
the Hybrid New Keynesian Phillips Curve. Journal of Monetary
Economics, 52(6), 1107-1118.
Gordon, R.J., 1997. The Time-Varying NAIRU and its Implications for
Economic Policy. Journal of Economic Perspectives, 11(1), 11-32.
Jondeau, E., Le Bihan, H. (2005). Testing For the New Keynesian Phillips
Curve. Additional International Evidence. Economic Modeling, 22(3),
521-550.
Kurmann, A. (2005). Quantifying the uncertainty about the fit of a New
Keynesian pricing Model. Journal of Monetary Economics, 52(6), 1119–
1134.
Lindé, J. (2005). Estimating New-Keynesian Phillips Curves: A Full
Information Maximum Likelihood Approach. Journal of Monetary
Economics, 52(6), 1135–1149.
Mankiw, N.G., 2001. The Inexorable and Mysterious Tradeoff between
Inflation and Unemployment. Economic Journal, 111(471-1), 45–61.
Mankiw, N.G., Reis, R. (2002). Sticky Information versus Sticky Prices: A
Proposal to Replace the New Keynesian Phillips Curve. Quarterly
Journal of Economics, 117(4), 1295–1328.
Mishkin, F.S. (2007). Inflation Dynamics. International Finance, 10(3), 317–
34.
Muth, J.F. (1961). Rational expectations and the theory of price movements,
Econometrica, 29(3), 315-335.
Rudd, J., Whelan, K. (2005). New Tests of the New-Keynesian Phillips
Tong & Kazuo
20
Curve. Journal of Monetary Economics, 52(6), 1167–1181.
Taylor, J.B. (1979). Staggered Wage Setting in a Macro Model. American
Economic Review, 69(2), 108–113.
Walsh, C. (2003). Monetary Theory and Policy (2nd Ed.). Cambridge, MA:
MIT Press.
Woodford, M. (2007). Interpreting inflation persistence: comments on the
conference on “Quantitative evidence on price determination”. Journal
of Money, Credit, and Banking, 39, 203–210.
Appendix A
Transforming Equation (2), we obtain the adjustment price level at time t
and time t+1 as follows:
1
11−
−−= ttt ppx
ρ
ρ
ρ (2’)
tttppx
ρ
ρ
ρ
−−=
++
1111 (2”)
Replacing ∗
tp of Equation (1), t
x of Equation (2’) and 1+tx of Equation
(2”) into Equation (3), we can obtain Equation (4):
( )tttttttt
ppEypppρ
ρ
ρ
ρβρπαρρ
ρ
ρ
ρ
2
111
1111 −−
−+++=
−−
+−−
( )111
21111
+−−
−++=
−−
−+− tttttt pEypp
ρ
ρβρπαρ
ρ
ρ
ρ
ρρ
ρ
Inflation Dynamics with Bounded Rationality
21
tttttttppEypp
ρ
ρ
ρ
ρβρπρα
ρ
ρ
ρ
ρ −−
−++=
−−
−+−−
1111111
11
11−+ ++
−=
−ttttt yE βρπαρπ
ρ
ρπ
ρ
ρ
1
22
111
−+−
+−
+= ttttt yE πρ
βρ
ρ
αρππ
Appendix B
According to Muth (1961), the rational expectations hypothesis means
that the expected inflation rate e
tπ is an unbiased predictor of the actual
inflation rate tπ , that is:
t
e
tt νππ += , 0=t
e
tE νπ , 0=tEν
Assuming that tν is independently and identically distributed normal with
variance 2σ , we know that
11 −− += ttt νππ
where 1−tν is a realized predicting error. Using two periods moving average
instead of tπ in the first equation, we get another predictor e
tπ~ below:
t
e
t
t
t
tt νπν
πππ
+=+=+ −
−− ~
22
11
1
The variance of predictor e
tπ~ is larger than that of e
tπ .
( ) ( ) 22
1
2
1
2
12
2
12
14
5
42
~ σππσννν
νν
νππ =−>=
−+=
−=− −−
−−− t
e
ttt
t
t
t
tt
e
t EEEE
Tong & Kazuo
22
Note that 01 =−ttE νν . It can be presumed easily that the more lag or lead
terms, the larger the variance of the predictor. This result is very appealing,
and will hold the generality when the distribution term bears the reproductive
property. For this reason, we select an instrument set only including one lag
and lead inflation rate to keep the variance of the predicting error to a
minimum.